论文标题
对串行依赖对惩罚回归方法的影响
On the Impact of Serial Dependence on Penalized Regression Methods
论文作者
论文摘要
本文表征了协变量串行依赖对惩罚回归（PRS）的非反应估计误差结合的影响。关注协变量之间的互相关程度与PRS的估计误差之间的直接关系，我们表明正交或较弱的交叉相关的固定AR过程可以表现出由串行依赖性引起的高伪相关性。在两个正交高斯AR（1）过程的情况下，我们为样品互相关的分布提供了分析结果，并通过广泛的仿真研究扩展和验证它们。此外，我们引入了一种新的程序，以减轻时间序列设置中的虚假相关性，并将PRS应用于预先使用的（ARMA过滤）时间序列。我们表明，在温和的假设下，我们的程序允许减少估计误差并制定有效的预测策略。我们的提案的估计准确性通过其他模拟进行了验证，以及对相对于欧元区的大量每月宏观经济时间序列的经验应用。
This paper characterizes the impact of covariate serial dependence on the non-asymptotic estimation error bound of penalized regressions (PRs). Focusing on the direct relationship between the degree of cross-correlation between covariates and the estimation error bound of PRs, we show that orthogonal or weakly cross-correlated stationary AR processes can exhibit high spurious correlations caused by serial dependence. We provide analytical results on the distribution of the sample cross-correlation in the case of two orthogonal Gaussian AR(1) processes, and extend and validate them through an extensive simulation study. Furthermore, we introduce a new procedure to mitigate spurious correlations in a time series setting, applying PRs to pre-whitened (ARMA filtered) time series. We show that under mild assumptions our procedure allows both to reduce the estimation error and to develop an effective forecasting strategy. The estimation accuracy of our proposal is validated through additional simulations, as well as an empirical application to a large set of monthly macroeconomic time series relative to the Euro Area.
